The mixing circuit electrically combines several series of signals to generate a single series of signals. As a document describing a general mixing circuit, an example is non-Patent Document 1.
FIG. 6 is a circuit diagram of showing a mixing circuit described in non-Patent Document 1. The mixing circuit described in FIG. 6 is composed of an output voltage signal generator 801, a frequency converter 802, an input unit 803, and a local oscillation signal generating circuit 5. The input unit 803 has an impedance matching circuit 2, and a signal output from a voltage signal source 9 is input through a signal source output impedance element 1 having an impedance value Z into the source of a grounded-gate MOS transistor M1 and the gate of a grounded-source MOS transistor M2 . The gate of the grounded-gate MOS transistor M1 and the gate of the grounded-source MOS transistor M2 are respectively biased to voltages Vb1 and Vb2, which are necessary for the MOS transistors M1 and M2 to each operate as a voltage-current converting element.
The drains of the grounded-gate MOS transistor M1 and the grounded-source MOS transistor M2 are connected to the sources of frequency converting MOS transistors M3 and M4, and M5 and M6, respectively. Local oscillation signals output from the local oscillation signal generating circuit 5 are input into the gates of the frequency converting MOS transistors M3 to M6.
The drains of the frequency converting MOS transistors M3 to M6 are connected to resistance elements 6 and 7 for current-voltage conversion. Connection points of the frequency converting MOS transistors M3 to M6 are output terminals 10a and 10b of the circuit shown in FIG. 6 (output voltages are indicated as differential voltage signals OUT+ and OUT−).
The above-described mixing circuit operates as follows. That is, in the input unit 803, an input signal Vin applies a voltage from the voltage signal source 9 through the signal source output impedance element 1 and the impedance matching circuit 2 to a node 8. Such an applied voltage is converted into currents having reversed phases by the grounded-gate MOS transistor M1 and the grounded-source MOS transistor M2, respectively. With such an operation, since a single-ended voltage signal is converted into a differential current signal, the input unit 803 corresponds to a single ended-differential signal converter.
The current generated by the input unit 803 is multiplied by the local oscillation signal generated by the local oscillation signal generating circuit 5 through the frequency converting MOS transistors M3, M4, M5, and M6, and then its frequency is converted to be current signals. The current signals are converted to voltage signals by the resistance elements 6 and 7, and are output from the output terminals 10a and 10b as the differential voltage signals OUT+ and OUT−.
It is to be noted that, however, when the frequency converting MOS transistors M3, M4, M5, and M6 each operate as an ideal switch, a non-linear component of the circuit shown in FIG. 6 is represented as follows. Specifically, according to the non-Patent Document 1, in order to calculate the non-linear component of the circuit, Vgs−Ids characteristics of a single unit of the MOS transistor are approximated as Expression (1). In addition, FIG. 7 shows the Vgs of a single unit of the MOS transistor.Ids=gm1×Vgs+gm3×Vgs3  Expression (1)
In the above Expression (1), Ids denotes drain current (variation from DC bias), Vgs denotes gate-source current (variation from DC bias), gm1 denotes first transconductance, and gm3 denotes third transconductance. In Expression (1), gm3×Vgs3 is a factor for generating a non-linear component.
Further, the input signal Vin is represented as Expression (2).Vin=A×cos(ωin×t)  Expression (2)
In the above Expression (2), A denotes amplitude of the input signal Vin, and ωin denotes frequency of the input signal Vin.
By use of the above Expression (1) and Expression (2), the calculation of the drain current of the grounded-gate MOS transistor M1 results in Expression (3).Ids—M1=−(½)×gm1—M1×Vin−( 1/16)×gm3—M1×Vin3  Expression (3)
In Expression (3), Ids—M1 denotes the drain current of the grounded-gate MOS transistor M1, gm1_M1 denotes the first transconductance of the grounded-gate MOS transistor M1, and gm3_M1 denotes the third transconductance of the grounded-gate MOS transistor M1.
Likewise, the calculation of the drain current of the grounded-source MOS transistor M2 results in Expression (4).Ids—M2=(½)×gm1—M2×Vin+(⅛)×gm3—M2×Vin3−( 1/16)×(gm1—M2/gm1—M1)×gm3—M2×Vin3  Expression (4)
In Expression (4), Ids—M2 denotes the drain current of the grounded-source MOS transistor M2, gm1_M2 denotes the first transconductance of the grounded-source MOS transistor M2, and gm3_M2 denotes the third transconductance of the grounded-source MOS transistor M2.
Here, the local oscillation signal VL0 to be input into the mixing circuit from the local oscillation signal generating circuit 5 is defined by Expression (5).VLO=ALO×cos(ωLO×t)  Expression (5)
In Expression (5), ALO denotes the amplitude of the local oscillation signal, and ωLO denotes the frequency of the local oscillation signal. The calculation of the differential output signal Vout—diff ((OUT+)−(OUT−)) of the mixing circuit in FIG. 6 results in Expression (6).Vout—diff=(gm1—M2+gm1—M1)×(½)×Gc1×R×A×Va+[(⅛)×gm3—M2−( 1/16)×(gm1—M2/gm1—M1)×gm3—M2+( 1/16)×gm3—M1]×Gc1×R×A3×Vb   Expression (6)
In Expression (6), Va and Vb are represented as follows.Va≈(½)×cos[(ωin±ωLO)×t]  Expression (6)-1Vb≈(¼)×cos[3×(ωin±ωLO)×t]  Expression (6)-2
In Expression (6), Gc1 denotes a conversion loss of the frequency in the frequency converting operation, and R is a resistance value of a load resistance for current-voltage conversion (resistance elements 6 and 7 in FIG. 6). In addition, the first term in Expression (6) represents an output signal component, and the second term thereof represents an output non-linear component. That is, the non-linear component of the mixing circuit shown in FIG. 6 is represented as the second term of Expression (6).
Next, the non-linear component calculated as described above will be analyzed. In a case where the grounded-gate MOS transistor M1 of the mixing circuit and the grounded-source MOS transistor M2 shown in FIG. 6 have an identical size (channel length and channel width) and an identical bias voltage is applied thereto, the transconductance of the grounded-gate MOS transistor M1 is same with that of the grounded-source MOS transistor M2. Therefore, the following Expression (7) and Expression (8) are satisfied.gm1_M1=gm1_M2  Expression (7)gm3_M1=gm3_M2  Expression (8)
When Expression (7) and Expression (8) are substituted into the second term of Expression (6), the following Expression (9) and Expression (10) in Expression (6) are same and cancel each other.−( 1/16)×(gm1_M2/gm1_M1)×gm3_M2  Expression (9)( 1/16)×gm3_M1  Expression (10)
Accordingly, the non-linear component (Non_Linear1) of the mixing circuit shown in FIG. 6 is represented as the following Expression (11). In Expression (11), the non-linear component (gm3_M2) of the grounded-source MOS transistor M2 is dominant.Non_Linear1=(⅛)×gm3—M2×Gc1×R×Vb  Expression (11)
Therefore, the description heretofore demonstrates that the linearity of the grounded-source MOS transistor M2 needs to be improved in order to decrease the non-linear component of the mixing circuit shown in FIG. 6.